Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T02:40:40.717Z Has data issue: false hasContentIssue false
  • English
  • Français

The free topological group on a cell complex

Published online by Cambridge University Press:  17 April 2009

J.P.L. Hardy
J.P.L. Hardy
Affiliation:
School of Mathematics and Computer Science, University College of North Wales, Bangor, Gwynedd, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is proved that the free k-group on a CW-complex X is itself a CW-complex containing X as a subcomplex. It follows, as a corollary, that the free topological group on a countable CW-complex is a countable CW-complex.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 455 - 463
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Brown, R. and Hardy, J.P.L., “Subgroups of free topological groups and free topological products of topological groups”, J. London Math. Soc. (to appear).Google Scholar
[2]Dowker, C.H., “Topology of metric complexes”, Amer. J. Math. 74 (1952), 555–577.CrossRefGoogle Scholar
[3]Graev, M.I., “Free topological groups”, Amer. Math. Soc. Transl. (1) 8 (1962), 305–364.Google Scholar
[4]Hardy, J.P.L., “Topological groupoids: coverings and universal constructions”, (PhD thesis, University College of North Wales, Bangor, 1974).Google Scholar
[5]Hardy, J.P.L., Morris, Sidney A. and Thompson, H.B., “Applications of the Stone-Čech compactification to free topological groups”, submitted.Google Scholar
[6]Lundell, Albert T. and Weingram, Stephen, The topology of CW complexes (The University Series in Higher Mathematics, 8. Van Nostrand Reinhold, New York, 1969).CrossRefGoogle Scholar
[7]Mack, John, Morris, Sidney A. and Ordman, Edward T., “Free topological groups and the projective dimension of a locally compact abelian group”, Proc. Amer. Math. Soc. 40 (1973), 303–308.CrossRefGoogle Scholar
[8]Markov, A.A., “On free topological groups”, Amer. Math. Soc. Transl. (1) 8 (1962), 195–272.Google Scholar
[9]McCord, M.C., “Classifying spaces and infinite symmetric products”, Trans. Amer. Math. Soc. 146 (1969), 273–298.CrossRefGoogle Scholar
[10]Ordman, Edward T., “Free products of topological groups which are kω–spaces”, Trans. Amer. Math. Soc. (to appear).Google Scholar
[11]Ordman, Edward T., “Free k–groups and free topological groups”, General Topology and Appl. (to appear).Google Scholar
[12]Thomas, Barbara V. Smith, “Free topological groups”, General Topology and Appl. 4 (1974), 51–72.CrossRefGoogle Scholar